The main objective of this paper is to develop an innovative methodology for the vibration suppression control of the multiple degrees-of-freedom (MDOF) flexible structure. The proposed structure represented in this research as a clamped-free-free-free truss type plate is rotated by motors. The controller has two loops for tracking and vibration suppression. In addition to stabilizing the actual system, the proposed feedback control is based on a genetic algorithm (GA) to seek the primary optimal control gain for tracking and stabilization purposes. Moreover, input shaping is introduced for the control scheme that limits motion-induced elastic vibration by shaping the reference command. Experimental results are presented, demonstrating that, in the control loop, roll and yaw angles track control and elastic mode stabilization. It was also demonstrated that combining the input shaper with the proportional-integral-derivative (PID) feedback method has been shown to yield improved performance in controlling the flexible structure system. The broad range of problems discussed in this research is valuable in civil, mechanical, and aerospace engineering for flexible structures with MDOM motion.